European leaders, led by Germany's chancellor, Angela Merkel, come to the crucial Docklands summit on Thursday believing they are winning or have won the argument about how to tackle casino capitalism.

The case pushed by Merkel repeatedly in recent weeks, and echoed by France and the European commission, is that there is no point now in more tax cuts and deficit spending to boost demand since it is not yet clear whether the huge fiscal stimuli packages already launched are actually going to work.

Rather, the Europeans argue, the focus should be on fixing a European and global system that is broke – through a new supervisory and regulatory regime. This option, Merkel declared at the weekend, offers the best chance of avoiding similar crises erupting once a decade, as has been the cycle since the 1980s.

"You are hugely mistaken if you think that this is just a storm and that we'll be back to the same old rules after a few difficult months," Frank-Walter Steinmeier, the German foreign minister, said at the weekend.

Ahead of the summit, the dispute has been about priorities. The Europeans have underlined their determination to prioritise regulation and supervision of the markets – a new "financial markets architecture" – over public spending and fiscal stimuli as the key to successful and sustainable recovery.

There is agreement on both sides of the Atlantic on the need for both regulation and public spending. The battle between the Europeans on the one hand and the US and Britain on the other for the past few months has been over emphasis and effectiveness and over which aspect should dominate – regulation or stimulus.

Six months before a tough general election, Merkel is refusing to back down, while all the signs are that the Obama White House and Downing Street are shifting to accommodate the German, and European, consensus.

The EU will be heavily represented at the G20, occupying more than one third of the seats – Britain, Germany, France, and Italy as well as Spain and the Netherlands plus the Czech EU presidency and José Manuel Barroso, the European commission chief.

They are all, with the exception of the British prime minister Gordon Brown, singing from the same hymn-sheet, although Mirek Topolánek, the lame duck Czech prime minister, was out of tune last week when he declared that European leaders were "alarmed" at the Obama administration's remedies for the financial and economic crisis.

But the European leaders are indeed worried that Obama's huge public spending programmes could fuel hyper-inflation and leave Europe struggling to refinance colossal levels of state debt if they followed suit.

After two decades of being lectured about the superiority of Wall Street and the City of London and preached to on the merits of untrammelled Anglo-American free markets, they also feel vindicated in their preference for the European social market economy model.

The G20 outcome, already drafted by Downing Street but not final, moots the possibility of a huge global fiscal stimulus worth $2tn (£1.4tn) which, the authors argue, would result in 2% growth in the world economy and the creation of 19 million jobs.

The declaration, according to the draft leaked to the German weekly Der Spiegel, also calls for regulation and supervision of "all financial markets, instruments and institutions, including hedge funds, which are systemically important", common guidelines for the remuneration of financial managers, and penalties for uncooperative tax havens.

David Miliband, the foreign secretary, said that the $2tnfigure was from a previous, discarded draft and that the figure referred not to new money, but to policies and pledges already announced.

But Michael Froman, a senior White House official dealing with the G20, continued to insist on fiscal stimulus, although the timing of countries' spending plans was left vague.

"First is putting in place significant stimulus to get growth going again," he told journalists at the weekend. "Secondly, fixing each of our financial systems to get lending flowing; third, avoiding protectionism; and fourth, taking steps to minimise the spread of the crisis to emerging markets and developing countries."

For the Europeans, the emphasis and the sequencing of policy moves here is troublesome, because there is a level of mistrust among the various leaders, and because the Europeans believe they will never have a better opportunity to get the sceptical US and Britain to deliver on tougher market rules.

But despite the persistent differences, rooted in cultures and history, Merkel also stresses that she is coming to London not to compete, but to cooperate.

And compared to the yawning gap that separated the parties only a few months ago, the EU and the Americans are converging on a consensus. In order to avoid failure or a damaging rift, though, the consensus taking shape is tending towards the minimalist.

In his speech to the European parliament last week in Strasbourg, Brown noted that there were European, British, and American proposals on the table on how to tackle the crisis, again exposing Britain's semi-detachment from the European mainstream.

But, in fact, the British proposals, from Lord Turner, the chairman of the Financial Services Authority, sit happily with the recommendations from the EU by Jacques de Larosière, the former treasury director at the French finance ministry. And the Europeans are also relieved by last week's announcement from Tim Geithner, the US treasury secretary, on a new regime for hedge funds, private equity firms, and the insurance markets.